The Order Dimension of Bruhat Order on Infinite Coxeter Groups

Nathan Reading, Debra J. Waugh

Abstract

We give a quadratic lower bound and a cubic upper bound on the order dimension of the Bruhat (or strong) ordering of the affine Coxeter group ${\tilde{A}}_n$. We also demonstrate that the order dimension of the Bruhat order is infinite for a large class of Coxeter groups.